Essays on VIX Futures and Options
Abstract: This thesis consists of three essays on VIX futures and options, and deals with issues highly relevant to all financial markets, such as understanding the operation of markets and developing flexible and tractable pricing models for contracts traded in them. It consists of four chapters. Chapter 1 provides a short introduction to the VIX and a brief explanation of how the old and new VIX are constructed. Thereafter, it discusses VIX derivatives and volatility strategy indexes, and presents other volatility indexes constructed by the Chicago Board Options Exchange. Finally, the chapter provides a short summary of each essay. Chapter 2 develops a term structure model for VIX futures. Instead of deriving the VIX futures price from a model for the instantaneous variance of the S&P 500 or a model for the VIX, the VIX futures price dynamics are specified exogenously. The empirical features of VIX futures returns (positive skewness, excess kurtosis and a decreasing volatility term structure for longer term expirations) are captured by assuming that they are normal inverse Gaussian distributed and scaled by a volatility function that is dependent on the maturity. The usefulness of the resulting model is illustrated in two applications: risk management (via calculating Value-at-Risk (VaR)) and asset pricing (via pricing hypothetical VIX options). The results show that the model provides a good fit for the empirical term structure of VIX futures, produces good VaR estimates, and is promising for use in pricing VIX options. Chapter 3 provides empirical evidence for long memory in the volatility process of VIX futures returns and investigates the practical importance of modelling it when calculating VaR for VIX futures and pricing VIX options. The analysis is performed using the GARCH, APARCH, FIGARCH and FIAPARCH models with the normal and skewed Student-t distributions. The VaR analysis shows that the long memory FIGARCH and FIAPARCH models produce the best out-of-sample VaR forecasts. The options analysis, however, suggests that the impact of long memory on the pricing of hypothetical VIX options is insignificant. Chapter 4 investigates the volatility-volume relation in the VIX futures market. Following [Giot, P., Laurent, S. and Petitjean, M., 2010, Trading activity, realized volatility and jumps, Journal of Empirical Finance, 17, 168-175], who examine the relation in the stock market, volatility is measured and decomposed into diffusion and jump components using the model-free realized volatility estimate. Consistent with the results of Giot et al. (2010), realized continuous (jump) volatility is found to be positively (negatively) related to volume.
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